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I need to find out the type of triangle (by the type of angles). Is triangle acute, right or obtuse, when the lenghts of triangle sides are:
a) 7, 8, 12
b) 20, 15, 40
c) 2/3, 8/9, 10/9

  • math -

    The largest angle is opposite the largest side.
    So all we have to do is check if the largest side is greater or smaller than a "hypotenuse"

    in 1st:
    7^2 + 8^2 = 113
    12^2 = 144
    so 12^2 > 7^2 + 8^2
    and the triangle is obtuse with the angle opposite 12 as > 90°

    2nd:
    a trick question!
    To form a triangle, the sum of any two sides has to be greater than the third side,
    but 20+15 is NOT greater than 40.
    So we can't even form the triangle.

    3rd:
    2/3, 8/9, 10/9
    or
    6/9, 8/9, 10/9
    this triangle has the same angles as
    6 , 8, 9 (they are similar)

    check for 9^2 vs 6^2 + 8^2

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